{"id":"https://openalex.org/W2159882399","doi":"https://doi.org/10.1137/s036301299731610x","title":"A State-Space Calculus for Rational Probability Density Functions and Applications to Non-Gaussian Filtering","display_name":"A State-Space Calculus for Rational Probability Density Functions and Applications to Non-Gaussian Filtering","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2159882399","doi":"https://doi.org/10.1137/s036301299731610x","mag":"2159882399"},"language":"en","primary_location":{"id":"doi:10.1137/s036301299731610x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s036301299731610x","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059144071","display_name":"Bernard Hanzon","orcid":"https://orcid.org/0000-0001-9085-0065"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bernard Hanzon","raw_affiliation_strings":["Department of Econometrics Free University De Boelelaan 1105 1081 HV Amsterdam The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Econometrics Free University De Boelelaan 1105 1081 HV Amsterdam The Netherlands","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038794787","display_name":"Raimund J. Ober","orcid":"https://orcid.org/0000-0002-1290-7430"},"institutions":[{"id":"https://openalex.org/I162577319","display_name":"The University of Texas at Dallas","ror":"https://ror.org/049emcs32","country_code":"US","type":"education","lineage":["https://openalex.org/I162577319"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Raimund J. Ober","raw_affiliation_strings":["Center for Engineering Mathematics EC35 University of Texas at Dallas Richardson, TX 75083 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Engineering Mathematics EC35 University of Texas at Dallas Richardson, TX 75083 USA","institution_ids":["https://openalex.org/I162577319"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2758,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.8956582,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"40","issue":"3","first_page":"724","last_page":"740"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10876","display_name":"Fault Detection and Control Systems","score":0.9914000034332275,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8526453971862793},{"id":"https://openalex.org/keywords/realization","display_name":"Realization (probability)","score":0.6924425363540649},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.6829162240028381},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.6743064522743225},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.6644027233123779},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5580527782440186},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.5186730623245239},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49965858459472656},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.4885757863521576},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.45339325070381165},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.43558216094970703},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.41738906502723694},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.41403117775917053},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2849069833755493},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1721230447292328},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08277150988578796},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07352343201637268}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8526453971862793},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.6924425363540649},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.6829162240028381},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.6743064522743225},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.6644027233123779},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5580527782440186},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.5186730623245239},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49965858459472656},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.4885757863521576},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.45339325070381165},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.43558216094970703},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.41738906502723694},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.41403117775917053},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2849069833755493},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1721230447292328},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08277150988578796},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07352343201637268},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/s036301299731610x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s036301299731610x","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:eprints.soton.ac.uk:424923","is_oa":false,"landing_page_url":"https://eprints.soton.ac.uk/424923/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:research.vu.nl:openaire_cris_publications/cee829a7-98f9-4dd5-a306-bfa52490a455","is_oa":false,"landing_page_url":"https://hdl.handle.net/1871.1/cee829a7-98f9-4dd5-a306-bfa52490a455","pdf_url":null,"source":{"id":"https://openalex.org/S4306401107","display_name":"VU Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Hanzon, B & Ober, R J 2001, 'A state-space calculus for rational probability density functions and applications to non-Gaussian filtering', SIAM Journal on Control and Optimization, vol. 40, pp. 724-740. https://doi.org/10.1137/S036301299731610X","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:research.vu.nl:publications/90cda2e7-c51c-43ee-8f80-adb3153411b5","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400546","display_name":"Digital Academic REpository of VU University Amsterdam (Vrije Universiteit Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I865915315","host_organization_name":"Vrije Universiteit Amsterdam","host_organization_lineage":["https://openalex.org/I865915315"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:vu:oai:research.vu.nl:publications/cee829a7-98f9-4dd5-a306-bfa52490a455","is_oa":false,"landing_page_url":"https://research.vu.nl/en/publications/cee829a7-98f9-4dd5-a306-bfa52490a455","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Control and Optimization, 40, 724 - 740. Society for Industrial and Applied Mathematics Publications","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7206540863","display_name":"Mathematical Sciences:Stabilization and Approximation of    Infinite Dimensional Systems","funder_award_id":"9501223","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W136674921","https://openalex.org/W1515569264","https://openalex.org/W1594563152","https://openalex.org/W2037371917","https://openalex.org/W2054599015","https://openalex.org/W2073038832","https://openalex.org/W2076209196","https://openalex.org/W2119305404","https://openalex.org/W2128978199","https://openalex.org/W2798813531","https://openalex.org/W3108418035","https://openalex.org/W3125246470"],"related_works":["https://openalex.org/W4319453045","https://openalex.org/W1642049914","https://openalex.org/W2893341095","https://openalex.org/W1484071118","https://openalex.org/W2016165693","https://openalex.org/W4243903653","https://openalex.org/W3092255988","https://openalex.org/W2889669269","https://openalex.org/W2089011113","https://openalex.org/W1462996453"],"abstract_inverted_index":{"We":[0],"propose":[1],"what":[2],"we":[3,58],"believe":[4],"to":[5,10,36],"be":[6,37],"a":[7,29,42,128],"novel":[8],"approach":[9],"performing":[11],"calculations":[12],"for":[13,82,104,127,146],"rational":[14,30,109,136],"density":[15,32,61,75,138],"functions":[16],"using":[17,69],"state-space":[18,102,142],"representations":[19],"of":[20,41,52,65,73,88,93,97,108,116,149,157],"the":[21,38,60,70,74,83,94,98,122,147,150],"densities.":[22,110],"By":[23],"standard":[24],"results":[25],"from":[26],"realization":[27],"theory,":[28],"probability":[31,137],"function":[33,40],"is":[34,55,67,115,125,160],"considered":[35],"transfer":[39],"linear":[43,129],"system":[44,54,131],"with":[45],"generally":[46],"complex":[47],"entries.":[48],"The":[49,63,155],"stable":[50],"part":[51],"this":[53],"positive-real,":[56],"which":[57,114],"call":[59],"summand.":[62,76],"existence":[64],"moments":[66,85],"investigated":[68,126],"Markov":[71,90],"parameters":[72],"Moreover,":[77],"explicit":[78,101],"formulae":[79],"are":[80,100,144],"given":[81],"existing":[84],"in":[86,118],"terms":[87],"these":[89],"parameters.":[91],"Some":[92],"main":[95],"contributions":[96],"paper":[99],"descriptions":[103],"products":[105],"and":[106,152],"convolutions":[107],"As":[111],"an":[112,163],"application":[113],"interest":[117],"its":[119],"own":[120],"right,":[121],"filtering":[123],"problem":[124],"time-varying":[130],"whose":[132],"noise":[133,159],"inputs":[134],"have":[135],"functions.":[139],"In":[140],"particular,":[141],"formulations":[143],"derived":[145],"calculation":[148],"prediction":[151],"update":[153],"equations.":[154],"case":[156],"Cauchy":[158],"treated":[161],"as":[162],"illustrative":[164],"example.":[165]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}